30 
On the Limits of the Optical 
bright disk surrounded by alternate bright and dark circles. The 
apparent breadth of these rings, reckoned from minimum to 
minimum, corresponds very nearly to a visual angle -whose sine is 
equal to - , where X expresses the respective wave-length of the 
light, and a the diameter of the opening. The outermost rings 
have exactly these dimensions, the inner are a little wider, and the 
radius of the innermost bright ring is 1 ' 220 — . Now, as the 
smallest visual angle under which we can possibly distinguish two 
fine bright lines from each other maybe fixed at.l minute, the 
figures of the brightest yellow-green hght, whose wave-length 
= 0-00055 mm., will be visible when = 1*89 mm. Even 
wdth a somewhat larger opening the dispersion of a bright point 
into a circle or of a bright line into a streak must be noticeable. 
When we look through such an aperture at any object which 
shows luminous points, the diffraction figures of the separate points 
partially cover each other, so that the fringe of dispersion circle of 
each single point, taken by itself, may not be recognizable. The 
efiect, however, of this diffraction, since it changes every point into 
a small dispersion circle, obviously causes effacement of the true 
outline, just as happens when the accommodation of the eye is 
imperfect, in consequence of which very minute objects, which can 
be perceived only when the image on the retina is sharply defined, 
are unrecognizable. We may convince ourselves that this is the 
fact by a simple experiment. The retina is most sensitively 
impressed by such objects as gratings, consisting of alternate dark 
and light parallel lines, whether printed on paper, or made of wire- 
work, or drawn on glass. Let the observer place himself at such a 
distance from the grating that, with the aid of spectacles giving 
perfect accommodation of the eye, he may just be able to distinguish 
the bars or lines separately from each other. Then let him place 
before his eye a card in which fine apertures of different diameters 
have been pierced, and observe whether he still sees the lines or 
sees them as well with as without the card. The grating must be 
brilliantly illuminated (e. g. by exposing lines printed on paper to 
direct sunlight), in order that the picture seen through the aperture 
may remain sufficiently bright. On trying the experiment myself, 
I find that a notable deterioration of the image is caused by an 
aperture of 1 * 72 mm. diameter, and the deterioration is much 
more striking with still narrower apertures. 
Instead of a series of lines printed letters may be used, the same 
conditions being fulfilled, namely, by observing the point at such a 
distance that the single letters may be just distinguished. On 
looking at them through an aperture of 1 mm. diameter, they will 
be scarcely or not at all legible. This experiment is, however, not 
